Properties

Label 441.4.e.x.226.3
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 19 x^{6} + 319 x^{4} + 798 x^{2} + 1764\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.3
Root \(-0.799027 - 1.38396i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.x.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(9.14584 - 15.8411i) q^{5} +21.4878 q^{8} +O(q^{10})\) \(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(9.14584 - 15.8411i) q^{5} +21.4878 q^{8} +(-14.6156 - 25.3149i) q^{10} +(-30.6336 - 53.0590i) q^{11} -32.4462 q^{13} +(-4.61555 + 7.99438i) q^{16} +(-40.6644 - 70.4329i) q^{17} +(-10.4542 + 18.1072i) q^{19} +99.6206 q^{20} -97.9084 q^{22} +(16.8655 - 29.2119i) q^{23} +(-104.793 - 181.507i) q^{25} +(-25.9254 + 44.9041i) q^{26} +52.0227 q^{29} +(96.9622 + 167.943i) q^{31} +(93.3271 + 161.647i) q^{32} -129.968 q^{34} +(133.578 - 231.363i) q^{37} +(16.7064 + 28.9364i) q^{38} +(196.524 - 340.390i) q^{40} -203.176 q^{41} -21.9520 q^{43} +(166.838 - 288.971i) q^{44} +(-26.9520 - 46.6822i) q^{46} +(-123.961 + 214.706i) q^{47} -334.929 q^{50} +(-88.3547 - 153.035i) q^{52} +(-70.4131 - 121.959i) q^{53} -1120.68 q^{55} +(41.5676 - 71.9971i) q^{58} +(-110.734 - 191.797i) q^{59} +(326.263 - 565.104i) q^{61} +309.902 q^{62} +224.435 q^{64} +(-296.748 + 513.983i) q^{65} +(-302.239 - 523.493i) q^{67} +(221.468 - 383.593i) q^{68} +716.031 q^{71} +(194.438 + 336.777i) q^{73} +(-213.465 - 369.731i) q^{74} -113.872 q^{76} +(144.871 - 250.923i) q^{79} +(84.4263 + 146.231i) q^{80} +(-162.343 + 281.186i) q^{82} +115.652 q^{83} -1487.64 q^{85} +(-17.5403 + 30.3806i) q^{86} +(-658.249 - 1140.12i) q^{88} +(469.682 - 813.513i) q^{89} +183.707 q^{92} +(198.096 + 343.112i) q^{94} +(191.225 + 331.212i) q^{95} -120.394 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{4} + O(q^{10}) \) \( 8q - 6q^{4} + 22q^{10} - 204q^{13} + 102q^{16} + 222q^{19} - 172q^{22} - 366q^{25} + 220q^{31} - 2040q^{34} + 374q^{37} + 822q^{40} - 1676q^{43} - 1716q^{46} - 40q^{52} - 5020q^{55} + 1694q^{58} + 1332q^{61} - 1372q^{64} - 1890q^{67} + 1750q^{73} - 4912q^{76} - 8q^{79} + 2480q^{82} - 2232q^{85} - 2682q^{88} - 1416q^{94} - 6020q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.799027 1.38396i 0.282499 0.489302i −0.689501 0.724285i \(-0.742170\pi\)
0.972000 + 0.234983i \(0.0755034\pi\)
\(3\) 0 0
\(4\) 2.72311 + 4.71657i 0.340389 + 0.589571i
\(5\) 9.14584 15.8411i 0.818029 1.41687i −0.0891033 0.996022i \(-0.528400\pi\)
0.907132 0.420846i \(-0.138267\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 21.4878 0.949635
\(9\) 0 0
\(10\) −14.6156 25.3149i −0.462184 0.800527i
\(11\) −30.6336 53.0590i −0.839672 1.45435i −0.890169 0.455630i \(-0.849414\pi\)
0.0504975 0.998724i \(-0.483919\pi\)
\(12\) 0 0
\(13\) −32.4462 −0.692228 −0.346114 0.938192i \(-0.612499\pi\)
−0.346114 + 0.938192i \(0.612499\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.61555 + 7.99438i −0.0721180 + 0.124912i
\(17\) −40.6644 70.4329i −0.580152 1.00485i −0.995461 0.0951718i \(-0.969660\pi\)
0.415309 0.909680i \(-0.363673\pi\)
\(18\) 0 0
\(19\) −10.4542 + 18.1072i −0.126230 + 0.218636i −0.922213 0.386682i \(-0.873621\pi\)
0.795983 + 0.605319i \(0.206954\pi\)
\(20\) 99.6206 1.11379
\(21\) 0 0
\(22\) −97.9084 −0.948825
\(23\) 16.8655 29.2119i 0.152900 0.264831i −0.779392 0.626536i \(-0.784472\pi\)
0.932292 + 0.361705i \(0.117805\pi\)
\(24\) 0 0
\(25\) −104.793 181.507i −0.838343 1.45205i
\(26\) −25.9254 + 44.9041i −0.195554 + 0.338709i
\(27\) 0 0
\(28\) 0 0
\(29\) 52.0227 0.333116 0.166558 0.986032i \(-0.446735\pi\)
0.166558 + 0.986032i \(0.446735\pi\)
\(30\) 0 0
\(31\) 96.9622 + 167.943i 0.561772 + 0.973017i 0.997342 + 0.0728626i \(0.0232135\pi\)
−0.435570 + 0.900155i \(0.643453\pi\)
\(32\) 93.3271 + 161.647i 0.515564 + 0.892983i
\(33\) 0 0
\(34\) −129.968 −0.655568
\(35\) 0 0
\(36\) 0 0
\(37\) 133.578 231.363i 0.593515 1.02800i −0.400240 0.916410i \(-0.631073\pi\)
0.993755 0.111587i \(-0.0355935\pi\)
\(38\) 16.7064 + 28.9364i 0.0713194 + 0.123529i
\(39\) 0 0
\(40\) 196.524 340.390i 0.776829 1.34551i
\(41\) −203.176 −0.773921 −0.386960 0.922096i \(-0.626475\pi\)
−0.386960 + 0.922096i \(0.626475\pi\)
\(42\) 0 0
\(43\) −21.9520 −0.0778523 −0.0389262 0.999242i \(-0.512394\pi\)
−0.0389262 + 0.999242i \(0.512394\pi\)
\(44\) 166.838 288.971i 0.571630 0.990092i
\(45\) 0 0
\(46\) −26.9520 46.6822i −0.0863882 0.149629i
\(47\) −123.961 + 214.706i −0.384713 + 0.666343i −0.991729 0.128346i \(-0.959033\pi\)
0.607016 + 0.794690i \(0.292366\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −334.929 −0.947324
\(51\) 0 0
\(52\) −88.3547 153.035i −0.235627 0.408117i
\(53\) −70.4131 121.959i −0.182490 0.316082i 0.760238 0.649645i \(-0.225082\pi\)
−0.942728 + 0.333563i \(0.891749\pi\)
\(54\) 0 0
\(55\) −1120.68 −2.74750
\(56\) 0 0
\(57\) 0 0
\(58\) 41.5676 71.9971i 0.0941050 0.162995i
\(59\) −110.734 191.797i −0.244344 0.423217i 0.717603 0.696453i \(-0.245239\pi\)
−0.961947 + 0.273236i \(0.911906\pi\)
\(60\) 0 0
\(61\) 326.263 565.104i 0.684815 1.18613i −0.288680 0.957426i \(-0.593216\pi\)
0.973495 0.228709i \(-0.0734503\pi\)
\(62\) 309.902 0.634800
\(63\) 0 0
\(64\) 224.435 0.438349
\(65\) −296.748 + 513.983i −0.566263 + 0.980796i
\(66\) 0 0
\(67\) −302.239 523.493i −0.551110 0.954551i −0.998195 0.0600592i \(-0.980871\pi\)
0.447085 0.894492i \(-0.352462\pi\)
\(68\) 221.468 383.593i 0.394954 0.684081i
\(69\) 0 0
\(70\) 0 0
\(71\) 716.031 1.19686 0.598431 0.801174i \(-0.295791\pi\)
0.598431 + 0.801174i \(0.295791\pi\)
\(72\) 0 0
\(73\) 194.438 + 336.777i 0.311743 + 0.539956i 0.978740 0.205105i \(-0.0657537\pi\)
−0.666996 + 0.745061i \(0.732420\pi\)
\(74\) −213.465 369.731i −0.335334 0.580816i
\(75\) 0 0
\(76\) −113.872 −0.171869
\(77\) 0 0
\(78\) 0 0
\(79\) 144.871 250.923i 0.206319 0.357355i −0.744233 0.667920i \(-0.767185\pi\)
0.950552 + 0.310565i \(0.100518\pi\)
\(80\) 84.4263 + 146.231i 0.117989 + 0.204363i
\(81\) 0 0
\(82\) −162.343 + 281.186i −0.218632 + 0.378681i
\(83\) 115.652 0.152946 0.0764728 0.997072i \(-0.475634\pi\)
0.0764728 + 0.997072i \(0.475634\pi\)
\(84\) 0 0
\(85\) −1487.64 −1.89832
\(86\) −17.5403 + 30.3806i −0.0219932 + 0.0380933i
\(87\) 0 0
\(88\) −658.249 1140.12i −0.797382 1.38111i
\(89\) 469.682 813.513i 0.559395 0.968901i −0.438152 0.898901i \(-0.644367\pi\)
0.997547 0.0699997i \(-0.0222998\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 183.707 0.208182
\(93\) 0 0
\(94\) 198.096 + 343.112i 0.217362 + 0.376482i
\(95\) 191.225 + 331.212i 0.206519 + 0.357701i
\(96\) 0 0
\(97\) −120.394 −0.126022 −0.0630110 0.998013i \(-0.520070\pi\)
−0.0630110 + 0.998013i \(0.520070\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 570.725 988.525i 0.570725 0.988525i
\(101\) 640.502 + 1109.38i 0.631013 + 1.09295i 0.987345 + 0.158587i \(0.0506938\pi\)
−0.356332 + 0.934359i \(0.615973\pi\)
\(102\) 0 0
\(103\) 265.669 460.153i 0.254147 0.440196i −0.710516 0.703681i \(-0.751539\pi\)
0.964664 + 0.263485i \(0.0848718\pi\)
\(104\) −697.198 −0.657364
\(105\) 0 0
\(106\) −225.048 −0.206213
\(107\) −66.6758 + 115.486i −0.0602411 + 0.104341i −0.894573 0.446922i \(-0.852520\pi\)
0.834332 + 0.551262i \(0.185854\pi\)
\(108\) 0 0
\(109\) 108.884 + 188.593i 0.0956811 + 0.165725i 0.909893 0.414844i \(-0.136164\pi\)
−0.814212 + 0.580568i \(0.802830\pi\)
\(110\) −895.455 + 1550.97i −0.776166 + 1.34436i
\(111\) 0 0
\(112\) 0 0
\(113\) −2006.09 −1.67006 −0.835031 0.550204i \(-0.814550\pi\)
−0.835031 + 0.550204i \(0.814550\pi\)
\(114\) 0 0
\(115\) −308.499 534.335i −0.250153 0.433278i
\(116\) 141.664 + 245.369i 0.113389 + 0.196396i
\(117\) 0 0
\(118\) −353.917 −0.276108
\(119\) 0 0
\(120\) 0 0
\(121\) −1211.34 + 2098.10i −0.910097 + 1.57633i
\(122\) −521.386 903.067i −0.386919 0.670163i
\(123\) 0 0
\(124\) −528.078 + 914.658i −0.382442 + 0.662409i
\(125\) −1547.22 −1.10710
\(126\) 0 0
\(127\) 1638.92 1.14512 0.572562 0.819861i \(-0.305950\pi\)
0.572562 + 0.819861i \(0.305950\pi\)
\(128\) −567.287 + 982.570i −0.391731 + 0.678498i
\(129\) 0 0
\(130\) 474.220 + 821.372i 0.319937 + 0.554147i
\(131\) 45.8755 79.4587i 0.0305967 0.0529950i −0.850322 0.526263i \(-0.823593\pi\)
0.880918 + 0.473268i \(0.156926\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −965.989 −0.622752
\(135\) 0 0
\(136\) −873.789 1513.45i −0.550932 0.954243i
\(137\) 933.564 + 1616.98i 0.582188 + 1.00838i 0.995220 + 0.0976621i \(0.0311364\pi\)
−0.413032 + 0.910717i \(0.635530\pi\)
\(138\) 0 0
\(139\) −639.778 −0.390397 −0.195199 0.980764i \(-0.562535\pi\)
−0.195199 + 0.980764i \(0.562535\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 572.128 990.955i 0.338112 0.585627i
\(143\) 993.946 + 1721.56i 0.581244 + 1.00674i
\(144\) 0 0
\(145\) 475.792 824.095i 0.272499 0.471982i
\(146\) 621.446 0.352269
\(147\) 0 0
\(148\) 1454.99 0.808103
\(149\) 1568.27 2716.32i 0.862264 1.49348i −0.00747495 0.999972i \(-0.502379\pi\)
0.869739 0.493513i \(-0.164287\pi\)
\(150\) 0 0
\(151\) 1360.68 + 2356.77i 0.733317 + 1.27014i 0.955458 + 0.295128i \(0.0953623\pi\)
−0.222141 + 0.975015i \(0.571304\pi\)
\(152\) −224.638 + 389.085i −0.119872 + 0.207625i
\(153\) 0 0
\(154\) 0 0
\(155\) 3547.20 1.83818
\(156\) 0 0
\(157\) 1439.87 + 2493.93i 0.731939 + 1.26776i 0.956053 + 0.293193i \(0.0947178\pi\)
−0.224114 + 0.974563i \(0.571949\pi\)
\(158\) −231.511 400.989i −0.116570 0.201905i
\(159\) 0 0
\(160\) 3414.22 1.68699
\(161\) 0 0
\(162\) 0 0
\(163\) −323.071 + 559.576i −0.155245 + 0.268892i −0.933148 0.359492i \(-0.882950\pi\)
0.777903 + 0.628384i \(0.216283\pi\)
\(164\) −553.271 958.293i −0.263434 0.456281i
\(165\) 0 0
\(166\) 92.4093 160.058i 0.0432069 0.0748366i
\(167\) 3765.03 1.74459 0.872296 0.488979i \(-0.162630\pi\)
0.872296 + 0.488979i \(0.162630\pi\)
\(168\) 0 0
\(169\) −1144.24 −0.520821
\(170\) −1188.67 + 2058.83i −0.536274 + 0.928854i
\(171\) 0 0
\(172\) −59.7777 103.538i −0.0265001 0.0458995i
\(173\) 1154.49 1999.64i 0.507366 0.878783i −0.492598 0.870257i \(-0.663953\pi\)
0.999964 0.00852600i \(-0.00271394\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 565.565 0.242222
\(177\) 0 0
\(178\) −750.577 1300.04i −0.316057 0.547427i
\(179\) −1516.88 2627.31i −0.633390 1.09706i −0.986854 0.161616i \(-0.948329\pi\)
0.353464 0.935448i \(-0.385004\pi\)
\(180\) 0 0
\(181\) 4079.71 1.67537 0.837686 0.546152i \(-0.183908\pi\)
0.837686 + 0.546152i \(0.183908\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 362.403 627.700i 0.145199 0.251493i
\(185\) −2443.36 4232.03i −0.971025 1.68186i
\(186\) 0 0
\(187\) −2491.40 + 4315.23i −0.974274 + 1.68749i
\(188\) −1350.24 −0.523809
\(189\) 0 0
\(190\) 611.177 0.233365
\(191\) 438.554 759.599i 0.166140 0.287762i −0.770920 0.636932i \(-0.780203\pi\)
0.937059 + 0.349170i \(0.113536\pi\)
\(192\) 0 0
\(193\) 729.356 + 1263.28i 0.272022 + 0.471155i 0.969379 0.245568i \(-0.0789744\pi\)
−0.697358 + 0.716723i \(0.745641\pi\)
\(194\) −96.1979 + 166.620i −0.0356011 + 0.0616629i
\(195\) 0 0
\(196\) 0 0
\(197\) −952.250 −0.344391 −0.172195 0.985063i \(-0.555086\pi\)
−0.172195 + 0.985063i \(0.555086\pi\)
\(198\) 0 0
\(199\) 1671.11 + 2894.44i 0.595285 + 1.03106i 0.993507 + 0.113774i \(0.0362941\pi\)
−0.398222 + 0.917289i \(0.630373\pi\)
\(200\) −2251.77 3900.18i −0.796120 1.37892i
\(201\) 0 0
\(202\) 2047.11 0.713041
\(203\) 0 0
\(204\) 0 0
\(205\) −1858.22 + 3218.52i −0.633090 + 1.09654i
\(206\) −424.554 735.349i −0.143593 0.248710i
\(207\) 0 0
\(208\) 149.757 259.387i 0.0499221 0.0864677i
\(209\) 1281.00 0.423966
\(210\) 0 0
\(211\) 1439.27 0.469589 0.234794 0.972045i \(-0.424558\pi\)
0.234794 + 0.972045i \(0.424558\pi\)
\(212\) 383.485 664.216i 0.124235 0.215182i
\(213\) 0 0
\(214\) 106.552 + 184.553i 0.0340361 + 0.0589522i
\(215\) −200.770 + 347.743i −0.0636855 + 0.110306i
\(216\) 0 0
\(217\) 0 0
\(218\) 348.007 0.108119
\(219\) 0 0
\(220\) −3051.74 5285.77i −0.935220 1.61985i
\(221\) 1319.41 + 2285.28i 0.401597 + 0.695587i
\(222\) 0 0
\(223\) −1009.86 −0.303253 −0.151626 0.988438i \(-0.548451\pi\)
−0.151626 + 0.988438i \(0.548451\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1602.92 + 2776.34i −0.471790 + 0.817165i
\(227\) 1474.30 + 2553.57i 0.431070 + 0.746635i 0.996966 0.0778419i \(-0.0248029\pi\)
−0.565896 + 0.824477i \(0.691470\pi\)
\(228\) 0 0
\(229\) −2019.42 + 3497.74i −0.582739 + 1.00933i 0.412414 + 0.910997i \(0.364686\pi\)
−0.995153 + 0.0983374i \(0.968648\pi\)
\(230\) −985.995 −0.282672
\(231\) 0 0
\(232\) 1117.85 0.316339
\(233\) 1497.90 2594.44i 0.421162 0.729473i −0.574892 0.818230i \(-0.694956\pi\)
0.996053 + 0.0887561i \(0.0282892\pi\)
\(234\) 0 0
\(235\) 2267.45 + 3927.34i 0.629413 + 1.09018i
\(236\) 603.081 1044.57i 0.166344 0.288117i
\(237\) 0 0
\(238\) 0 0
\(239\) 1810.28 0.489948 0.244974 0.969530i \(-0.421221\pi\)
0.244974 + 0.969530i \(0.421221\pi\)
\(240\) 0 0
\(241\) −1874.71 3247.10i −0.501083 0.867900i −0.999999 0.00125048i \(-0.999602\pi\)
0.498917 0.866650i \(-0.333731\pi\)
\(242\) 1935.79 + 3352.88i 0.514203 + 0.890625i
\(243\) 0 0
\(244\) 3553.80 0.932414
\(245\) 0 0
\(246\) 0 0
\(247\) 339.200 587.512i 0.0873797 0.151346i
\(248\) 2083.50 + 3608.74i 0.533478 + 0.924012i
\(249\) 0 0
\(250\) −1236.27 + 2141.28i −0.312754 + 0.541706i
\(251\) −2706.96 −0.680724 −0.340362 0.940295i \(-0.610550\pi\)
−0.340362 + 0.940295i \(0.610550\pi\)
\(252\) 0 0
\(253\) −2066.61 −0.513544
\(254\) 1309.54 2268.20i 0.323496 0.560312i
\(255\) 0 0
\(256\) 1804.29 + 3125.13i 0.440502 + 0.762971i
\(257\) −2687.64 + 4655.13i −0.652337 + 1.12988i 0.330218 + 0.943905i \(0.392878\pi\)
−0.982554 + 0.185975i \(0.940456\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3232.31 −0.770998
\(261\) 0 0
\(262\) −73.3116 126.979i −0.0172870 0.0299420i
\(263\) 2623.28 + 4543.66i 0.615051 + 1.06530i 0.990376 + 0.138406i \(0.0441979\pi\)
−0.375324 + 0.926893i \(0.622469\pi\)
\(264\) 0 0
\(265\) −2575.95 −0.597129
\(266\) 0 0
\(267\) 0 0
\(268\) 1646.06 2851.06i 0.375184 0.649837i
\(269\) −1506.66 2609.61i −0.341496 0.591489i 0.643214 0.765686i \(-0.277600\pi\)
−0.984711 + 0.174197i \(0.944267\pi\)
\(270\) 0 0
\(271\) 3448.62 5973.19i 0.773022 1.33891i −0.162877 0.986646i \(-0.552077\pi\)
0.935899 0.352267i \(-0.114589\pi\)
\(272\) 750.756 0.167358
\(273\) 0 0
\(274\) 2983.77 0.657869
\(275\) −6420.37 + 11120.4i −1.40787 + 2.43850i
\(276\) 0 0
\(277\) −1659.30 2874.00i −0.359920 0.623400i 0.628027 0.778191i \(-0.283863\pi\)
−0.987947 + 0.154792i \(0.950529\pi\)
\(278\) −511.200 + 885.424i −0.110287 + 0.191022i
\(279\) 0 0
\(280\) 0 0
\(281\) −6274.14 −1.33197 −0.665986 0.745964i \(-0.731989\pi\)
−0.665986 + 0.745964i \(0.731989\pi\)
\(282\) 0 0
\(283\) 3886.24 + 6731.16i 0.816300 + 1.41387i 0.908391 + 0.418122i \(0.137311\pi\)
−0.0920914 + 0.995751i \(0.529355\pi\)
\(284\) 1949.83 + 3377.21i 0.407399 + 0.705635i
\(285\) 0 0
\(286\) 3176.76 0.656803
\(287\) 0 0
\(288\) 0 0
\(289\) −850.695 + 1473.45i −0.173152 + 0.299908i
\(290\) −760.341 1316.95i −0.153961 0.266669i
\(291\) 0 0
\(292\) −1058.95 + 1834.16i −0.212228 + 0.367590i
\(293\) −854.897 −0.170456 −0.0852280 0.996361i \(-0.527162\pi\)
−0.0852280 + 0.996361i \(0.527162\pi\)
\(294\) 0 0
\(295\) −4051.02 −0.799523
\(296\) 2870.29 4971.49i 0.563623 0.976223i
\(297\) 0 0
\(298\) −2506.17 4340.82i −0.487177 0.843815i
\(299\) −547.222 + 947.817i −0.105842 + 0.183323i
\(300\) 0 0
\(301\) 0 0
\(302\) 4348.89 0.828645
\(303\) 0 0
\(304\) −96.5041 167.150i −0.0182069 0.0315352i
\(305\) −5967.90 10336.7i −1.12040 1.94058i
\(306\) 0 0
\(307\) −2550.68 −0.474185 −0.237092 0.971487i \(-0.576194\pi\)
−0.237092 + 0.971487i \(0.576194\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2834.31 4909.17i 0.519284 0.899427i
\(311\) 3740.25 + 6478.31i 0.681962 + 1.18119i 0.974381 + 0.224903i \(0.0722064\pi\)
−0.292419 + 0.956290i \(0.594460\pi\)
\(312\) 0 0
\(313\) 3.12392 5.41079i 0.000564135 0.000977111i −0.865743 0.500488i \(-0.833154\pi\)
0.866307 + 0.499511i \(0.166487\pi\)
\(314\) 4601.99 0.827088
\(315\) 0 0
\(316\) 1578.00 0.280915
\(317\) −482.902 + 836.410i −0.0855598 + 0.148194i −0.905630 0.424070i \(-0.860601\pi\)
0.820070 + 0.572263i \(0.193935\pi\)
\(318\) 0 0
\(319\) −1593.64 2760.27i −0.279708 0.484469i
\(320\) 2052.64 3555.28i 0.358582 0.621083i
\(321\) 0 0
\(322\) 0 0
\(323\) 1700.46 0.292929
\(324\) 0 0
\(325\) 3400.13 + 5889.20i 0.580324 + 1.00515i
\(326\) 516.285 + 894.232i 0.0877129 + 0.151923i
\(327\) 0 0
\(328\) −4365.80 −0.734942
\(329\) 0 0
\(330\) 0 0
\(331\) −3355.10 + 5811.20i −0.557139 + 0.964992i 0.440595 + 0.897706i \(0.354767\pi\)
−0.997734 + 0.0672865i \(0.978566\pi\)
\(332\) 314.934 + 545.482i 0.0520610 + 0.0901723i
\(333\) 0 0
\(334\) 3008.36 5210.64i 0.492845 0.853633i
\(335\) −11056.9 −1.80330
\(336\) 0 0
\(337\) −605.546 −0.0978819 −0.0489409 0.998802i \(-0.515585\pi\)
−0.0489409 + 0.998802i \(0.515585\pi\)
\(338\) −914.281 + 1583.58i −0.147131 + 0.254839i
\(339\) 0 0
\(340\) −4051.02 7016.57i −0.646168 1.11920i
\(341\) 5940.61 10289.4i 0.943408 1.63403i
\(342\) 0 0
\(343\) 0 0
\(344\) −471.700 −0.0739313
\(345\) 0 0
\(346\) −1844.94 3195.53i −0.286660 0.496510i
\(347\) −3469.08 6008.62i −0.536686 0.929567i −0.999080 0.0428923i \(-0.986343\pi\)
0.462394 0.886675i \(-0.346991\pi\)
\(348\) 0 0
\(349\) −10368.9 −1.59035 −0.795176 0.606378i \(-0.792622\pi\)
−0.795176 + 0.606378i \(0.792622\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 5717.90 9903.69i 0.865809 1.49963i
\(353\) −2940.88 5093.75i −0.443420 0.768026i 0.554521 0.832170i \(-0.312902\pi\)
−0.997941 + 0.0641440i \(0.979568\pi\)
\(354\) 0 0
\(355\) 6548.70 11342.7i 0.979068 1.69580i
\(356\) 5115.98 0.761647
\(357\) 0 0
\(358\) −4848.11 −0.715728
\(359\) −294.634 + 510.322i −0.0433153 + 0.0750244i −0.886870 0.462019i \(-0.847125\pi\)
0.843555 + 0.537043i \(0.180459\pi\)
\(360\) 0 0
\(361\) 3210.92 + 5561.47i 0.468132 + 0.810829i
\(362\) 3259.80 5646.14i 0.473291 0.819763i
\(363\) 0 0
\(364\) 0 0
\(365\) 7113.21 1.02006
\(366\) 0 0
\(367\) −1774.36 3073.28i −0.252373 0.437122i 0.711806 0.702376i \(-0.247878\pi\)
−0.964179 + 0.265254i \(0.914544\pi\)
\(368\) 155.687 + 269.658i 0.0220537 + 0.0381982i
\(369\) 0 0
\(370\) −7809.25 −1.09725
\(371\) 0 0
\(372\) 0 0
\(373\) 790.667 1369.47i 0.109756 0.190104i −0.805915 0.592031i \(-0.798326\pi\)
0.915672 + 0.401927i \(0.131660\pi\)
\(374\) 3981.39 + 6895.97i 0.550462 + 0.953429i
\(375\) 0 0
\(376\) −2663.64 + 4613.56i −0.365337 + 0.632783i
\(377\) −1687.94 −0.230592
\(378\) 0 0
\(379\) 3057.01 0.414322 0.207161 0.978307i \(-0.433578\pi\)
0.207161 + 0.978307i \(0.433578\pi\)
\(380\) −1041.46 + 1803.85i −0.140594 + 0.243515i
\(381\) 0 0
\(382\) −700.834 1213.88i −0.0938685 0.162585i
\(383\) −5289.87 + 9162.33i −0.705744 + 1.22238i 0.260678 + 0.965426i \(0.416054\pi\)
−0.966422 + 0.256959i \(0.917280\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2331.10 0.307383
\(387\) 0 0
\(388\) −327.846 567.845i −0.0428965 0.0742989i
\(389\) 3696.65 + 6402.78i 0.481819 + 0.834534i 0.999782 0.0208684i \(-0.00664310\pi\)
−0.517964 + 0.855403i \(0.673310\pi\)
\(390\) 0 0
\(391\) −2743.31 −0.354821
\(392\) 0 0
\(393\) 0 0
\(394\) −760.874 + 1317.87i −0.0972900 + 0.168511i
\(395\) −2649.93 4589.81i −0.337550 0.584654i
\(396\) 0 0
\(397\) 889.086 1539.94i 0.112398 0.194679i −0.804339 0.594171i \(-0.797480\pi\)
0.916737 + 0.399492i \(0.130814\pi\)
\(398\) 5341.04 0.672669
\(399\) 0 0
\(400\) 1934.71 0.241839
\(401\) 73.8031 127.831i 0.00919090 0.0159191i −0.861393 0.507938i \(-0.830408\pi\)
0.870584 + 0.492019i \(0.163741\pi\)
\(402\) 0 0
\(403\) −3146.06 5449.13i −0.388874 0.673550i
\(404\) −3488.31 + 6041.94i −0.429579 + 0.744053i
\(405\) 0 0
\(406\) 0 0
\(407\) −16367.9 −1.99343
\(408\) 0 0
\(409\) −1080.03 1870.66i −0.130572 0.226157i 0.793325 0.608798i \(-0.208348\pi\)
−0.923897 + 0.382641i \(0.875015\pi\)
\(410\) 2969.53 + 5143.37i 0.357694 + 0.619544i
\(411\) 0 0
\(412\) 2893.79 0.346036
\(413\) 0 0
\(414\) 0 0
\(415\) 1057.74 1832.05i 0.125114 0.216704i
\(416\) −3028.11 5244.84i −0.356888 0.618148i
\(417\) 0 0
\(418\) 1023.56 1772.85i 0.119770 0.207447i
\(419\) 13491.0 1.57298 0.786488 0.617605i \(-0.211897\pi\)
0.786488 + 0.617605i \(0.211897\pi\)
\(420\) 0 0
\(421\) −14146.7 −1.63769 −0.818847 0.574012i \(-0.805386\pi\)
−0.818847 + 0.574012i \(0.805386\pi\)
\(422\) 1150.01 1991.88i 0.132658 0.229771i
\(423\) 0 0
\(424\) −1513.02 2620.63i −0.173299 0.300163i
\(425\) −8522.69 + 14761.7i −0.972732 + 1.68482i
\(426\) 0 0
\(427\) 0 0
\(428\) −726.262 −0.0820215
\(429\) 0 0
\(430\) 320.841 + 555.712i 0.0359821 + 0.0623229i
\(431\) 4544.26 + 7870.89i 0.507864 + 0.879646i 0.999959 + 0.00910411i \(0.00289797\pi\)
−0.492095 + 0.870542i \(0.663769\pi\)
\(432\) 0 0
\(433\) −15461.2 −1.71597 −0.857986 0.513673i \(-0.828284\pi\)
−0.857986 + 0.513673i \(0.828284\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −593.009 + 1027.12i −0.0651376 + 0.112822i
\(437\) 352.632 + 610.776i 0.0386010 + 0.0668590i
\(438\) 0 0
\(439\) −891.091 + 1543.41i −0.0968780 + 0.167798i −0.910391 0.413749i \(-0.864219\pi\)
0.813513 + 0.581547i \(0.197552\pi\)
\(440\) −24081.0 −2.60913
\(441\) 0 0
\(442\) 4216.97 0.453803
\(443\) 6712.36 11626.1i 0.719896 1.24690i −0.241145 0.970489i \(-0.577523\pi\)
0.961041 0.276407i \(-0.0891437\pi\)
\(444\) 0 0
\(445\) −8591.27 14880.5i −0.915203 1.58518i
\(446\) −806.907 + 1397.60i −0.0856685 + 0.148382i
\(447\) 0 0
\(448\) 0 0
\(449\) −418.639 −0.0440018 −0.0220009 0.999758i \(-0.507004\pi\)
−0.0220009 + 0.999758i \(0.507004\pi\)
\(450\) 0 0
\(451\) 6224.02 + 10780.3i 0.649839 + 1.12555i
\(452\) −5462.80 9461.85i −0.568470 0.984619i
\(453\) 0 0
\(454\) 4712.03 0.487107
\(455\) 0 0
\(456\) 0 0
\(457\) 354.205 613.501i 0.0362560 0.0627973i −0.847328 0.531070i \(-0.821790\pi\)
0.883584 + 0.468273i \(0.155123\pi\)
\(458\) 3227.15 + 5589.59i 0.329246 + 0.570271i
\(459\) 0 0
\(460\) 1680.15 2910.11i 0.170299 0.294966i
\(461\) 8223.97 0.830865 0.415432 0.909624i \(-0.363630\pi\)
0.415432 + 0.909624i \(0.363630\pi\)
\(462\) 0 0
\(463\) −9414.17 −0.944954 −0.472477 0.881343i \(-0.656640\pi\)
−0.472477 + 0.881343i \(0.656640\pi\)
\(464\) −240.114 + 415.889i −0.0240237 + 0.0416103i
\(465\) 0 0
\(466\) −2393.73 4146.05i −0.237955 0.412151i
\(467\) 5410.76 9371.72i 0.536146 0.928632i −0.462961 0.886379i \(-0.653213\pi\)
0.999107 0.0422535i \(-0.0134537\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7247.02 0.711234
\(471\) 0 0
\(472\) −2379.43 4121.29i −0.232038 0.401902i
\(473\) 672.470 + 1164.75i 0.0653704 + 0.113225i
\(474\) 0 0
\(475\) 4382.11 0.423295
\(476\) 0 0
\(477\) 0 0
\(478\) 1446.47 2505.35i 0.138410 0.239733i
\(479\) −4092.75 7088.85i −0.390402 0.676196i 0.602100 0.798420i \(-0.294331\pi\)
−0.992503 + 0.122224i \(0.960997\pi\)
\(480\) 0 0
\(481\) −4334.09 + 7506.87i −0.410848 + 0.711609i
\(482\) −5991.79 −0.566221
\(483\) 0 0
\(484\) −13194.4 −1.23915
\(485\) −1101.10 + 1907.17i −0.103090 + 0.178557i
\(486\) 0 0
\(487\) 2001.58 + 3466.83i 0.186242 + 0.322581i 0.943994 0.329961i \(-0.107036\pi\)
−0.757752 + 0.652543i \(0.773702\pi\)
\(488\) 7010.67 12142.8i 0.650324 1.12639i
\(489\) 0 0
\(490\) 0 0
\(491\) 11180.8 1.02766 0.513831 0.857891i \(-0.328226\pi\)
0.513831 + 0.857891i \(0.328226\pi\)
\(492\) 0 0
\(493\) −2115.47 3664.11i −0.193258 0.334733i
\(494\) −542.060 938.876i −0.0493693 0.0855101i
\(495\) 0 0
\(496\) −1790.14 −0.162056
\(497\) 0 0
\(498\) 0 0
\(499\) 1885.54 3265.85i 0.169155 0.292985i −0.768968 0.639287i \(-0.779229\pi\)
0.938123 + 0.346302i \(0.112563\pi\)
\(500\) −4213.24 7297.55i −0.376844 0.652713i
\(501\) 0 0
\(502\) −2162.93 + 3746.31i −0.192304 + 0.333080i
\(503\) 13597.2 1.20531 0.602654 0.798003i \(-0.294110\pi\)
0.602654 + 0.798003i \(0.294110\pi\)
\(504\) 0 0
\(505\) 23431.7 2.06475
\(506\) −1651.28 + 2860.09i −0.145075 + 0.251278i
\(507\) 0 0
\(508\) 4462.97 + 7730.08i 0.389788 + 0.675132i
\(509\) 3680.38 6374.60i 0.320491 0.555106i −0.660099 0.751179i \(-0.729485\pi\)
0.980589 + 0.196073i \(0.0628188\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −3309.87 −0.285698
\(513\) 0 0
\(514\) 4295.00 + 7439.16i 0.368569 + 0.638380i
\(515\) −4859.54 8416.97i −0.415800 0.720186i
\(516\) 0 0
\(517\) 15189.5 1.29213
\(518\) 0 0
\(519\) 0 0
\(520\) −6376.46 + 11044.4i −0.537743 + 0.931398i
\(521\) 6899.40 + 11950.1i 0.580169 + 1.00488i 0.995459 + 0.0951930i \(0.0303468\pi\)
−0.415290 + 0.909689i \(0.636320\pi\)
\(522\) 0 0
\(523\) 9423.58 16322.1i 0.787886 1.36466i −0.139373 0.990240i \(-0.544509\pi\)
0.927260 0.374419i \(-0.122158\pi\)
\(524\) 499.697 0.0416591
\(525\) 0 0
\(526\) 8384.29 0.695005
\(527\) 7885.83 13658.7i 0.651826 1.12900i
\(528\) 0 0
\(529\) 5514.61 + 9551.58i 0.453243 + 0.785040i
\(530\) −2058.25 + 3565.00i −0.168688 + 0.292177i
\(531\) 0 0
\(532\) 0 0
\(533\) 6592.29 0.535730
\(534\) 0 0
\(535\) 1219.61 + 2112.43i 0.0985579 + 0.170707i
\(536\) −6494.45 11248.7i −0.523354 0.906475i
\(537\) 0 0
\(538\) −4815.44 −0.385889
\(539\) 0 0
\(540\) 0 0
\(541\) 7234.77 12531.0i 0.574948 0.995839i −0.421099 0.907015i \(-0.638356\pi\)
0.996047 0.0888248i \(-0.0283111\pi\)
\(542\) −5511.09 9545.49i −0.436756 0.756483i
\(543\) 0 0
\(544\) 7590.19 13146.6i 0.598211 1.03613i
\(545\) 3983.36 0.313080
\(546\) 0 0
\(547\) 5749.63 0.449427 0.224713 0.974425i \(-0.427855\pi\)
0.224713 + 0.974425i \(0.427855\pi\)
\(548\) −5084.39 + 8806.43i −0.396340 + 0.686482i
\(549\) 0 0
\(550\) 10260.1 + 17771.0i 0.795441 + 1.37774i
\(551\) −543.857 + 941.988i −0.0420492 + 0.0728313i
\(552\) 0 0
\(553\) 0 0
\(554\) −5303.31 −0.406708
\(555\) 0 0
\(556\) −1742.19 3017.55i −0.132887 0.230167i
\(557\) −2715.39 4703.19i −0.206561 0.357775i 0.744068 0.668104i \(-0.232894\pi\)
−0.950629 + 0.310330i \(0.899561\pi\)
\(558\) 0 0
\(559\) 712.260 0.0538915
\(560\) 0 0
\(561\) 0 0
\(562\) −5013.21 + 8683.14i −0.376280 + 0.651737i
\(563\) −12065.3 20897.8i −0.903185 1.56436i −0.823335 0.567556i \(-0.807889\pi\)
−0.0798500 0.996807i \(-0.525444\pi\)
\(564\) 0 0
\(565\) −18347.4 + 31778.6i −1.36616 + 2.36626i
\(566\) 12420.8 0.922415
\(567\) 0 0
\(568\) 15385.9 1.13658
\(569\) −9024.27 + 15630.5i −0.664880 + 1.15161i 0.314437 + 0.949278i \(0.398184\pi\)
−0.979318 + 0.202328i \(0.935149\pi\)
\(570\) 0 0
\(571\) 5637.42 + 9764.30i 0.413168 + 0.715628i 0.995234 0.0975136i \(-0.0310889\pi\)
−0.582066 + 0.813141i \(0.697756\pi\)
\(572\) −5413.25 + 9376.02i −0.395698 + 0.685369i
\(573\) 0 0
\(574\) 0 0
\(575\) −7069.54 −0.512731
\(576\) 0 0
\(577\) −12047.5 20866.8i −0.869225 1.50554i −0.862790 0.505562i \(-0.831285\pi\)
−0.00643457 0.999979i \(-0.502048\pi\)
\(578\) 1359.46 + 2354.65i 0.0978303 + 0.169447i
\(579\) 0 0
\(580\) 5182.53 0.371022
\(581\) 0 0
\(582\) 0 0
\(583\) −4314.02 + 7472.10i −0.306464 + 0.530811i
\(584\) 4178.05 + 7236.59i 0.296043 + 0.512761i
\(585\) 0 0
\(586\) −683.086 + 1183.14i −0.0481536 + 0.0834045i
\(587\) −11438.9 −0.804315 −0.402157 0.915571i \(-0.631740\pi\)
−0.402157 + 0.915571i \(0.631740\pi\)
\(588\) 0 0
\(589\) −4054.66 −0.283649
\(590\) −3236.87 + 5606.43i −0.225864 + 0.391208i
\(591\) 0 0
\(592\) 1233.07 + 2135.74i 0.0856063 + 0.148274i
\(593\) −2087.22 + 3615.17i −0.144539 + 0.250349i −0.929201 0.369575i \(-0.879503\pi\)
0.784662 + 0.619924i \(0.212837\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 17082.2 1.17402
\(597\) 0 0
\(598\) 874.491 + 1514.66i 0.0598003 + 0.103577i
\(599\) 5727.77 + 9920.79i 0.390702 + 0.676715i 0.992542 0.121901i \(-0.0388991\pi\)
−0.601841 + 0.798616i \(0.705566\pi\)
\(600\) 0 0
\(601\) 17539.2 1.19042 0.595208 0.803572i \(-0.297070\pi\)
0.595208 + 0.803572i \(0.297070\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −7410.59 + 12835.5i −0.499226 + 0.864685i
\(605\) 22157.4 + 38377.8i 1.48897 + 2.57898i
\(606\) 0 0
\(607\) 1692.86 2932.12i 0.113198 0.196064i −0.803860 0.594818i \(-0.797224\pi\)
0.917058 + 0.398754i \(0.130557\pi\)
\(608\) −3902.65 −0.260318
\(609\) 0 0
\(610\) −19074.1 −1.26604
\(611\) 4022.06 6966.41i 0.266309 0.461261i
\(612\) 0 0
\(613\) −2135.94 3699.56i −0.140734 0.243758i 0.787039 0.616903i \(-0.211613\pi\)
−0.927773 + 0.373145i \(0.878279\pi\)
\(614\) −2038.06 + 3530.02i −0.133957 + 0.232020i
\(615\) 0 0
\(616\) 0 0
\(617\) −13123.9 −0.856321 −0.428160 0.903703i \(-0.640838\pi\)
−0.428160 + 0.903703i \(0.640838\pi\)
\(618\) 0 0
\(619\) −946.969 1640.20i −0.0614893 0.106503i 0.833642 0.552305i \(-0.186252\pi\)
−0.895131 + 0.445803i \(0.852918\pi\)
\(620\) 9659.43 + 16730.6i 0.625697 + 1.08374i
\(621\) 0 0
\(622\) 11954.3 0.770614
\(623\) 0 0
\(624\) 0 0
\(625\) −1051.49 + 1821.23i −0.0672952 + 0.116559i
\(626\) −4.99219 8.64673i −0.000318735 0.000552066i
\(627\) 0 0
\(628\) −7841.87 + 13582.5i −0.498288 + 0.863060i
\(629\) −21727.5 −1.37731
\(630\) 0 0
\(631\) 20443.8 1.28979 0.644894 0.764272i \(-0.276902\pi\)
0.644894 + 0.764272i \(0.276902\pi\)
\(632\) 3112.95 5391.79i 0.195928 0.339357i
\(633\) 0 0
\(634\) 771.703 + 1336.63i 0.0483411 + 0.0837292i
\(635\) 14989.3 25962.3i 0.936745 1.62249i
\(636\) 0 0
\(637\) 0 0
\(638\) −5093.46 −0.316069
\(639\) 0 0
\(640\) 10376.6 + 17972.9i 0.640895 + 1.11006i
\(641\) 9614.27 + 16652.4i 0.592419 + 1.02610i 0.993906 + 0.110235i \(0.0351604\pi\)
−0.401486 + 0.915865i \(0.631506\pi\)
\(642\) 0 0
\(643\) 18525.1 1.13617 0.568087 0.822969i \(-0.307684\pi\)
0.568087 + 0.822969i \(0.307684\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1358.71 2353.36i 0.0827522 0.143331i
\(647\) −4011.20 6947.60i −0.243735 0.422161i 0.718040 0.696001i \(-0.245039\pi\)
−0.961775 + 0.273840i \(0.911706\pi\)
\(648\) 0 0
\(649\) −6784.36 + 11750.9i −0.410338 + 0.710726i
\(650\) 10867.2 0.655764
\(651\) 0 0
\(652\) −3519.03 −0.211374
\(653\) 1025.85 1776.82i 0.0614769 0.106481i −0.833649 0.552295i \(-0.813752\pi\)
0.895126 + 0.445814i \(0.147086\pi\)
\(654\) 0 0
\(655\) −839.141 1453.43i −0.0500579 0.0867029i
\(656\) 937.770 1624.26i 0.0558136 0.0966721i
\(657\) 0 0
\(658\) 0 0
\(659\) −14765.2 −0.872792 −0.436396 0.899755i \(-0.643745\pi\)
−0.436396 + 0.899755i \(0.643745\pi\)
\(660\) 0 0
\(661\) 323.532 + 560.374i 0.0190377 + 0.0329743i 0.875387 0.483422i \(-0.160606\pi\)
−0.856350 + 0.516397i \(0.827273\pi\)
\(662\) 5361.63 + 9286.62i 0.314782 + 0.545218i
\(663\) 0 0
\(664\) 2485.11 0.145243
\(665\) 0 0
\(666\) 0 0
\(667\) 877.390 1519.68i 0.0509335 0.0882195i
\(668\) 10252.6 + 17758.0i 0.593840 + 1.02856i
\(669\) 0 0
\(670\) −8834.78 + 15302.3i −0.509429 + 0.882357i
\(671\) −39978.5 −2.30008
\(672\) 0 0
\(673\) −22596.6 −1.29426 −0.647130 0.762380i \(-0.724031\pi\)
−0.647130 + 0.762380i \(0.724031\pi\)
\(674\) −483.848 + 838.049i −0.0276515 + 0.0478938i
\(675\) 0 0
\(676\) −3115.90 5396.90i −0.177282 0.307061i
\(677\) −12602.1 + 21827.5i −0.715420 + 1.23914i 0.247377 + 0.968919i \(0.420431\pi\)
−0.962797 + 0.270225i \(0.912902\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −31966.2 −1.80272
\(681\) 0 0
\(682\) −9493.42 16443.1i −0.533023 0.923223i
\(683\) −8510.27 14740.2i −0.476774 0.825796i 0.522872 0.852411i \(-0.324860\pi\)
−0.999646 + 0.0266151i \(0.991527\pi\)
\(684\) 0 0
\(685\) 34152.9 1.90499
\(686\) 0 0
\(687\) 0 0
\(688\) 101.321 175.493i 0.00561456 0.00972470i
\(689\) 2284.64 + 3957.11i 0.126325 + 0.218801i
\(690\) 0 0
\(691\) −9645.26 + 16706.1i −0.531003 + 0.919724i 0.468342 + 0.883547i \(0.344851\pi\)
−0.999345 + 0.0361772i \(0.988482\pi\)
\(692\) 12575.2 0.690806
\(693\) 0 0
\(694\) −11087.6 −0.606452
\(695\) −5851.31 + 10134.8i −0.319356 + 0.553142i
\(696\) 0 0
\(697\) 8262.04 + 14310.3i 0.448991 + 0.777676i
\(698\) −8285.01 + 14350.1i −0.449273 + 0.778163i
\(699\) 0 0
\(700\) 0 0
\(701\) 28511.4 1.53618 0.768088 0.640345i \(-0.221208\pi\)
0.768088 + 0.640345i \(0.221208\pi\)
\(702\) 0 0
\(703\) 2792.90 + 4837.45i 0.149838 + 0.259528i
\(704\) −6875.25 11908.3i −0.368069 0.637515i
\(705\) 0 0
\(706\) −9399.37 −0.501062
\(707\) 0 0
\(708\) 0 0
\(709\) −14213.3 + 24618.1i −0.752877 + 1.30402i 0.193546 + 0.981091i \(0.438001\pi\)
−0.946423 + 0.322930i \(0.895332\pi\)
\(710\) −10465.2 18126.2i −0.553171 0.958120i
\(711\) 0 0
\(712\) 10092.4 17480.6i 0.531221 0.920102i
\(713\) 6541.27 0.343580
\(714\) 0 0
\(715\) 36361.9 1.90190
\(716\) 8261.26 14308.9i 0.431198 0.746857i
\(717\) 0 0
\(718\) 470.842 + 815.522i 0.0244731 + 0.0423886i
\(719\) −10881.7 + 18847.6i −0.564420 + 0.977603i 0.432684 + 0.901546i \(0.357567\pi\)
−0.997103 + 0.0760577i \(0.975767\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10262.4 0.528987
\(723\) 0 0
\(724\) 11109.5 + 19242.2i 0.570278 + 0.987750i
\(725\) −5451.61 9442.47i −0.279266 0.483703i
\(726\) 0 0
\(727\) 13422.8 0.684763 0.342382 0.939561i \(-0.388766\pi\)
0.342382 + 0.939561i \(0.388766\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 5683.65 9844.36i 0.288166 0.499118i
\(731\) 892.666 + 1546.14i 0.0451661 + 0.0782301i
\(732\) 0 0
\(733\) 2279.76 3948.66i 0.114877 0.198973i −0.802854 0.596176i \(-0.796686\pi\)
0.917731 + 0.397204i \(0.130019\pi\)
\(734\) −5671.04 −0.285180
\(735\) 0 0
\(736\) 6296.04 0.315319
\(737\) −18517.4 + 32073.0i −0.925503 + 1.60302i
\(738\) 0 0
\(739\) 18332.7 + 31753.2i 0.912557 + 1.58059i 0.810439 + 0.585823i \(0.199228\pi\)
0.102118 + 0.994772i \(0.467438\pi\)
\(740\) 13307.1 23048.6i 0.661052 1.14498i
\(741\) 0 0
\(742\) 0 0
\(743\) −10321.3 −0.509625 −0.254813 0.966990i \(-0.582014\pi\)
−0.254813 + 0.966990i \(0.582014\pi\)
\(744\) 0 0
\(745\) −28686.2 49686.0i −1.41071 2.44343i
\(746\) −1263.53 2188.50i −0.0620121 0.107408i
\(747\) 0 0
\(748\) −27137.4 −1.32653
\(749\) 0 0
\(750\) 0 0
\(751\) 13339.0 23103.9i 0.648134 1.12260i −0.335434 0.942064i \(-0.608883\pi\)
0.983568 0.180537i \(-0.0577836\pi\)
\(752\) −1144.30 1981.98i −0.0554896 0.0961107i
\(753\) 0 0
\(754\) −1348.71 + 2336.03i −0.0651421 + 0.112829i
\(755\) 49778.4 2.39950
\(756\) 0 0
\(757\) −11630.8 −0.558425 −0.279212 0.960229i \(-0.590073\pi\)
−0.279212 + 0.960229i \(0.590073\pi\)
\(758\) 2442.63 4230.77i 0.117045 0.202729i
\(759\) 0 0
\(760\) 4109.01 + 7117.02i 0.196118 + 0.339686i
\(761\) 18045.8 31256.3i 0.859607 1.48888i −0.0126976 0.999919i \(-0.504042\pi\)
0.872304 0.488963i \(-0.162625\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4776.93 0.226208
\(765\) 0 0
\(766\) 8453.51 + 14641.9i 0.398744 + 0.690644i
\(767\) 3592.89 + 6223.07i 0.169142 + 0.292962i
\(768\) 0 0
\(769\) −33089.3 −1.55167 −0.775833 0.630938i \(-0.782670\pi\)
−0.775833 + 0.630938i \(0.782670\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3972.23 + 6880.11i −0.185186 + 0.320752i
\(773\) −15495.4 26838.8i −0.720997 1.24880i −0.960601 0.277933i \(-0.910351\pi\)
0.239603 0.970871i \(-0.422983\pi\)
\(774\) 0 0
\(775\) 20321.9 35198.6i 0.941915 1.63144i
\(776\) −2587.00 −0.119675
\(777\) 0 0
\(778\) 11814.9 0.544453
\(779\) 2124.05 3678.96i 0.0976917 0.169207i
\(780\) 0 0
\(781\) −21934.6 37991.9i −1.00497 1.74066i
\(782\) −2191.98 + 3796.62i −0.100236 + 0.173615i
\(783\) 0 0
\(784\) 0 0
\(785\) 52675.4 2.39499
\(786\) 0 0
\(787\) −12710.6 22015.4i −0.575711 0.997161i −0.995964 0.0897537i \(-0.971392\pi\)
0.420253 0.907407i \(-0.361941\pi\)
\(788\) −2593.08 4491.35i −0.117227 0.203043i
\(789\) 0 0
\(790\) −8469.46 −0.381430
\(791\) 0 0
\(792\) 0 0